Notation for a graph without any edges? Is there a standard notation for a graph (on a given set of vertices) without any edges?
 A: There are many ways to define a graph, but a pretty standard one is a pair $(V,E)$ where $V$ is a finite set of points and $E \subset \binom{V}{2}$.  So, what you are looking for is $(V, \emptyset)$; which would be pretty widely understood.
A: I don't think there is standard notation for this. If you've already fixed a notation for complement (say a superscript c) then you could use $K_n^c$. But I don't think standard notation exists for this.
A: Some people call it the empty graph on n vertices.
A: I have seen $\bar{K}_n$ for the graph with n vertices and no edges, but I do not remember where.
A: I suppose $n\cdot K_1$ assuming of course that $n \ge 1$. In the event that there are also no vertices it is sometimes called the Null Graph although F. Harary, F. and R. Read in "Is the Null Graph a Pointless Concept?" suggest that it may be more trouble than it is worth in that it has too many edges to be a tree, no automorphism group etc.
A: I have seen it written as $E_n$, where E stands for empty.
A: Standard notation in graph theory? In category theory the analogous thing can be denoted $disc(V)$ where $V$ is the set of vertices.
